General Relativity and Quantum Cosmology (gr-qc)

Abstract: Phase transition is a very enlightening topic in black hole physics, which can largely demonstrate a certain quantum property of gravity. In this study, we use complex analysis to study the phase transition of the black hole thermodynamics system. By decomposing the obtained winding number, we can predict some characteristics of the phase transition of the system. There are three basic elements: (1) when the winding number is one, there is no phase transition, and the corresponding complex structure is the Riemann surface with one foliation; (2) the winding number is two, which corresponds to the second-order phase transition and has a Riemann surface with double foliations; (3) when the winding number is three, it means that the first order phase transition will occur, accompanied by the second order phase transition, which has a Riemann surface with three foliations. Especially, a black hole thermodynamics system with a triple point has a structure of the Riemann surface with five foliations.

Abstract: Boson Stars are, at present, hypothetical compact stellar objects whose existence, however, could resolve several enigmas of current astrophysics. If they exist, either as independent astrophysical entities or as a matter admixture of more standard compact stars, then their imprints can probably be observed in the not-too-distant future from the gravitational signal of coalescing binaries in current and future GW detectors. Here we show that the multipole moments of rotating boson stars obey certain universal relations, valid for a broad set of models and various states in terms of the \textit{harmonic indices}. These universal relations are equivalent to a kind of no-hair theorem for this exotic matter, allowing to map these universal (i.e. model independent) multipoles to an equally universal gravitational field around the stellar object. Further, the multipole moments can be related to observable astrophysical quantities.

Abstract: In this chapter, we discuss recent work on precision Earth laboratory tests of different aspects of gravity. In particular the discussion is focused on those tests that can be used to probe hypothesis for physics beyond Newtonian gravity and General Relativity. The latter includes tests of foundations like local Lorentz invariance, Weak-Equivalence Principle tests, short-range gravity tests, gravimeter-type tests, and other frontier possibilities like the free-fall of anti-matter and searches for non-Riemann gravity effects. The focus is on key results in theory, phenomenology, and experiment in the last few decades. We describe the motivations for continued interest in precision tests of gravity in the laboratory, including the possibility to search for physics beyond General Relativity. Test frameworks for describing deviations from General Relativity are emphasized, including ones based on effective field theory, allowing for generic violations of Lorentz symmetry, CPT symmetry, and diffeomorphism symmetry.